/// <summary>
/// Tìm phần tử nghịch đảo trên vành Zn
/// </summary>
/// <param name="n">A big integer</param>
/// <returns>A big integer</returns>
public BigInteger ModInverse(BigInteger n)
{
BigInteger m = new BigInteger(n);
BigInteger a = new BigInteger(this);
BigInteger y0 = new BigInteger(0);
BigInteger y1 = new BigInteger(1);
BigInteger r, q, y = new BigInteger(1);
while (a > 0)
{
r = m % a;
if (r == 0) break;
q = m / a;
y = y0 - y1 * q;
m = a;
a = r;
y0 = y1;
y1 = y;
}
if (a > 1) throw (new ArithmeticException("No inverse!"));
if (y > 0)
return y;
else
return y + n;
}
/// <summary>
/// Tính a^x mod n
/// </summary>
/// <param name="exp">The exponent</param>
/// <param name="n">A big Integer</param>
/// <returns>A big Integer</returns>
public BigInteger ModExp(BigInteger x, BigInteger n)
{
if (x<1)
throw (new ArithmeticException("Positive exponents only."));
BigInteger r = new BigInteger(1);
BigInteger a = new BigInteger(this);
while (x > 0)
{
if((x & 1) == 1)
{
r = (r * a) % n;
}
a = (a * a) % n;
x >>= 1;
}
return r;
}
static void deszyfrowanie()
{
Console.WriteLine("podaj nazwe pliku do odszyfrowania");
string we = Console.ReadLine();
string wy = we.Replace(".rsa", "");
BinaryReader br = new BinaryReader(File.Open(we, FileMode.Open));
BinaryWriter bw = new BinaryWriter(File.Open(wy, FileMode.Create));
int blocksize = keysize / 8;
long blockcount = (br.BaseStream.Length / blocksize);
bctl = blockcount.ToString().Length;
for (long i = 0; i < blockcount; i++) {
byte[] buf = br.ReadBytes(blocksize);
BigInteger bi = new BigInteger(buf);
BigInteger bo = decode(bi);
buf = bo.getBytes();
if (i != (blockcount - 1))
buf = buf.pad(blocksize - 1);
bw.Write(buf);
//drawTextProgressBar(i, blockcount);
}
bw.Close();
Console.WriteLine("zapisano pod nazwa {0}", wy);
}
//***********************************************************************
// Overloading of unary << operators
//***********************************************************************
public static BigInteger operator <<(BigInteger bi1, int shiftVal)
{
BigInteger result = new BigInteger(bi1);
result.dataLength = shiftLeft(result.data, shiftVal);
return result;
}
//***********************************************************************
// Overloading of the unary -- operator
//***********************************************************************
public static BigInteger operator --(BigInteger bi1)
{
BigInteger result = new BigInteger(bi1);
long val;
bool carryIn = true;
int index = 0;
while (carryIn && index < maxLength)
{
val = (long)(result.data[index]);
val--;
result.data[index] = (uint)(val & 0xFFFFFFFF);
if (val >= 0)
carryIn = false;
index++;
}
if (index > result.dataLength)
result.dataLength = index;
while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
result.dataLength--;
// overflow check
int lastPos = maxLength - 1;
// overflow if initial value was -ve but -- caused a sign
// change to positive.
if ((bi1.data[lastPos] & 0x80000000) != 0 &&
(result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000))
{
throw (new ArithmeticException("Underflow in --."));
}
return result;
}
//***********************************************************************
// Overloading of multiplication operator
//***********************************************************************
public static BigInteger operator *(BigInteger bi1, BigInteger bi2)
{
int lastPos = maxLength - 1;
bool bi1Neg = false, bi2Neg = false;
// take the absolute value of the inputs
try
{
if ((bi1.data[lastPos] & 0x80000000) != 0) // bi1 negative
{
bi1Neg = true; bi1 = -bi1;
}
if ((bi2.data[lastPos] & 0x80000000) != 0) // bi2 negative
{
bi2Neg = true; bi2 = -bi2;
}
}
catch (Exception) { }
BigInteger result = new BigInteger();
// multiply the absolute values
try
{
for (int i = 0; i < bi1.dataLength; i++)
{
if (bi1.data[i] == 0) continue;
ulong mcarry = 0;
for (int j = 0, k = i; j < bi2.dataLength; j++, k++)
{
// k = i + j
ulong val = ((ulong)bi1.data[i] * (ulong)bi2.data[j]) +
(ulong)result.data[k] + mcarry;
result.data[k] = (uint)(val & 0xFFFFFFFF);
mcarry = (val >> 32);
}
if (mcarry != 0)
result.data[i + bi2.dataLength] = (uint)mcarry;
}
}
catch (Exception)
{
throw (new ArithmeticException("Multiplication overflow."));
}
result.dataLength = bi1.dataLength + bi2.dataLength;
if (result.dataLength > maxLength)
result.dataLength = maxLength;
while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
result.dataLength--;
// overflow check (result is -ve)
if ((result.data[lastPos] & 0x80000000) != 0)
{
if (bi1Neg != bi2Neg && result.data[lastPos] == 0x80000000) // different sign
{
// handle the special case where multiplication produces
// a max negative number in 2's complement.
if (result.dataLength == 1)
return result;
else
{
bool isMaxNeg = true;
for (int i = 0; i < result.dataLength - 1 && isMaxNeg; i++)
{
if (result.data[i] != 0)
isMaxNeg = false;
}
if (isMaxNeg)
return result;
}
}
throw (new ArithmeticException("Multiplication overflow."));
}
// if input has different signs, then result is -ve
if (bi1Neg != bi2Neg)
return -result;
return result;
}
//***********************************************************************
// Generates a random number with the specified number of bits such
// that gcd(number, this) = 1
//***********************************************************************
public BigInteger genCoPrime(int bits, Random rand)
{
bool done = false;
BigInteger result = new BigInteger();
while (!done)
{
result.genRandomBits(bits, rand);
//Console.WriteLine(result.ToString(16));
// gcd test
BigInteger g = result.gcd(this);
if (g.dataLength == 1 && g.data[0] == 1)
done = true;
}
return result;
}
private bool LucasStrongTestHelper(BigInteger thisVal)
{
// Do the test (selects D based on Selfridge)
// Let D be the first element of the sequence
// 5, -7, 9, -11, 13, ... for which J(D,n) = -1
// Let P = 1, Q = (1-D) / 4
long D = 5, sign = -1, dCount = 0;
bool done = false;
while (!done)
{
int Jresult = BigInteger.Jacobi(D, thisVal);
if (Jresult == -1)
done = true; // J(D, this) = 1
else
{
if (Jresult == 0 && Math.Abs(D) < thisVal) // divisor found
return false;
if (dCount == 20)
{
// check for square
BigInteger root = thisVal.sqrt();
if (root * root == thisVal)
return false;
}
//Console.WriteLine(D);
D = (Math.Abs(D) + 2) * sign;
sign = -sign;
}
dCount++;
}
long Q = (1 - D) >> 2;
/*
Console.WriteLine("D = " + D);
Console.WriteLine("Q = " + Q);
Console.WriteLine("(n,D) = " + thisVal.gcd(D));
Console.WriteLine("(n,Q) = " + thisVal.gcd(Q));
Console.WriteLine("J(D|n) = " + BigInteger.Jacobi(D, thisVal));
*/
BigInteger p_add1 = thisVal + 1;
int s = 0;
for (int index = 0; index < p_add1.dataLength; index++)
{
uint mask = 0x01;
for (int i = 0; i < 32; i++)
{
if ((p_add1.data[index] & mask) != 0)
{
index = p_add1.dataLength; // to break the outer loop
break;
}
mask <<= 1;
s++;
}
}
BigInteger t = p_add1 >> s;
// calculate constant = b^(2k) / m
// for Barrett Reduction
BigInteger constant = new BigInteger();
int nLen = thisVal.dataLength << 1;
constant.data[nLen] = 0x00000001;
constant.dataLength = nLen + 1;
constant = constant / thisVal;
BigInteger[] lucas = LucasSequenceHelper(1, Q, t, thisVal, constant, 0);
bool isPrime = false;
if ((lucas[0].dataLength == 1 && lucas[0].data[0] == 0) ||
(lucas[1].dataLength == 1 && lucas[1].data[0] == 0))
{
// u(t) = 0 or V(t) = 0
isPrime = true;
}
for (int i = 1; i < s; i++)
{
if (!isPrime)
{
// doubling of index
lucas[1] = thisVal.BarrettReduction(lucas[1] * lucas[1], thisVal, constant);
lucas[1] = (lucas[1] - (lucas[2] << 1)) % thisVal;
//lucas[1] = ((lucas[1] * lucas[1]) - (lucas[2] << 1)) % thisVal;
if ((lucas[1].dataLength == 1 && lucas[1].data[0] == 0))
isPrime = true;
}
lucas[2] = thisVal.BarrettReduction(lucas[2] * lucas[2], thisVal, constant); //Q^k
}
if (isPrime) // additional checks for composite numbers
{
// If n is prime and gcd(n, Q) == 1, then
// Q^((n+1)/2) = Q * Q^((n-1)/2) is congruent to (Q * J(Q, n)) mod n
BigInteger g = thisVal.gcd(Q);
if (g.dataLength == 1 && g.data[0] == 1) // gcd(this, Q) == 1
{
if ((lucas[2].data[maxLength - 1] & 0x80000000) != 0)
lucas[2] += thisVal;
BigInteger temp = (Q * BigInteger.Jacobi(Q, thisVal)) % thisVal;
if ((temp.data[maxLength - 1] & 0x80000000) != 0)
temp += thisVal;
if (lucas[2] != temp)
isPrime = false;
}
}
return isPrime;
}
//***********************************************************************
// Overloading of the NEGATE operator (2's complement)
//***********************************************************************
public static BigInteger operator -(BigInteger bi1)
{
// handle neg of zero separately since it'll cause an overflow
// if we proceed.
if (bi1.dataLength == 1 && bi1.data[0] == 0)
return (new BigInteger());
BigInteger result = new BigInteger(bi1);
// 1's complement
for (int i = 0; i < maxLength; i++)
result.data[i] = (uint)(~(bi1.data[i]));
// add one to result of 1's complement
long val, carry = 1;
int index = 0;
while (carry != 0 && index < maxLength)
{
val = (long)(result.data[index]);
val++;
result.data[index] = (uint)(val & 0xFFFFFFFF);
carry = val >> 32;
index++;
}
if ((bi1.data[maxLength - 1] & 0x80000000) == (result.data[maxLength - 1] & 0x80000000))
throw (new ArithmeticException("Overflow in negation.\n"));
result.dataLength = maxLength;
while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
result.dataLength--;
return result;
}
public MyBigInt(BigInteger b)
: base(b)
{
}
//***********************************************************************
// Tests the correct implementation of the modulo exponential function
// using RSA encryption and decryption (using pre-computed encryption and
// decryption keys).
//***********************************************************************
public static void RSATest(int rounds)
{
Random rand = new Random(1);
byte[] val = new byte[64];
// private and public key
BigInteger bi_e = new BigInteger("a932b948feed4fb2b692609bd22164fc9edb59fae7880cc1eaff7b3c9626b7e5b241c27a974833b2622ebe09beb451917663d47232488f23a117fc97720f1e7", 16);
BigInteger bi_d = new BigInteger("4adf2f7a89da93248509347d2ae506d683dd3a16357e859a980c4f77a4e2f7a01fae289f13a851df6e9db5adaa60bfd2b162bbbe31f7c8f828261a6839311929d2cef4f864dde65e556ce43c89bbbf9f1ac5511315847ce9cc8dc92470a747b8792d6a83b0092d2e5ebaf852c85cacf34278efa99160f2f8aa7ee7214de07b7", 16);
BigInteger bi_n = new BigInteger("e8e77781f36a7b3188d711c2190b560f205a52391b3479cdb99fa010745cbeba5f2adc08e1de6bf38398a0487c4a73610d94ec36f17f3f46ad75e17bc1adfec99839589f45f95ccc94cb2a5c500b477eb3323d8cfab0c8458c96f0147a45d27e45a4d11d54d77684f65d48f15fafcc1ba208e71e921b9bd9017c16a5231af7f", 16);
Console.WriteLine("e =\n" + bi_e.ToString(10));
Console.WriteLine("\nd =\n" + bi_d.ToString(10));
Console.WriteLine("\nn =\n" + bi_n.ToString(10) + "\n");
for (int count = 0; count < rounds; count++)
{
// generate data of random length
int t1 = 0;
while (t1 == 0)
t1 = (int)(rand.NextDouble() * 65);
bool done = false;
while (!done)
{
for (int i = 0; i < 64; i++)
{
if (i < t1)
val[i] = (byte)(rand.NextDouble() * 256);
else
val[i] = 0;
if (val[i] != 0)
done = true;
}
}
while (val[0] == 0)
val[0] = (byte)(rand.NextDouble() * 256);
Console.Write("Round = " + count);
// encrypt and decrypt data
BigInteger bi_data = new BigInteger(val, t1);
BigInteger bi_encrypted = bi_data.modPow(bi_e, bi_n);
BigInteger bi_decrypted = bi_encrypted.modPow(bi_d, bi_n);
// compare
if (bi_decrypted != bi_data)
{
Console.WriteLine("\nError at round " + count);
Console.WriteLine(bi_data + "\n");
return;
}
Console.WriteLine(" <PASSED>.");
}
}
//***********************************************************************
// Tests the correct implementation of the modulo exponential and
// inverse modulo functions using RSA encryption and decryption. The two
// pseudoprimes p and q are fixed, but the two RSA keys are generated
// for each round of testing.
//***********************************************************************
public static void RSATest2(int rounds)
{
Random rand = new Random();
byte[] val = new byte[64];
byte[] pseudoPrime1 = {
(byte)0x85, (byte)0x84, (byte)0x64, (byte)0xFD, (byte)0x70, (byte)0x6A,
(byte)0x9F, (byte)0xF0, (byte)0x94, (byte)0x0C, (byte)0x3E, (byte)0x2C,
(byte)0x74, (byte)0x34, (byte)0x05, (byte)0xC9, (byte)0x55, (byte)0xB3,
(byte)0x85, (byte)0x32, (byte)0x98, (byte)0x71, (byte)0xF9, (byte)0x41,
(byte)0x21, (byte)0x5F, (byte)0x02, (byte)0x9E, (byte)0xEA, (byte)0x56,
(byte)0x8D, (byte)0x8C, (byte)0x44, (byte)0xCC, (byte)0xEE, (byte)0xEE,
(byte)0x3D, (byte)0x2C, (byte)0x9D, (byte)0x2C, (byte)0x12, (byte)0x41,
(byte)0x1E, (byte)0xF1, (byte)0xC5, (byte)0x32, (byte)0xC3, (byte)0xAA,
(byte)0x31, (byte)0x4A, (byte)0x52, (byte)0xD8, (byte)0xE8, (byte)0xAF,
(byte)0x42, (byte)0xF4, (byte)0x72, (byte)0xA1, (byte)0x2A, (byte)0x0D,
(byte)0x97, (byte)0xB1, (byte)0x31, (byte)0xB3,
};
byte[] pseudoPrime2 = {
(byte)0x99, (byte)0x98, (byte)0xCA, (byte)0xB8, (byte)0x5E, (byte)0xD7,
(byte)0xE5, (byte)0xDC, (byte)0x28, (byte)0x5C, (byte)0x6F, (byte)0x0E,
(byte)0x15, (byte)0x09, (byte)0x59, (byte)0x6E, (byte)0x84, (byte)0xF3,
(byte)0x81, (byte)0xCD, (byte)0xDE, (byte)0x42, (byte)0xDC, (byte)0x93,
(byte)0xC2, (byte)0x7A, (byte)0x62, (byte)0xAC, (byte)0x6C, (byte)0xAF,
(byte)0xDE, (byte)0x74, (byte)0xE3, (byte)0xCB, (byte)0x60, (byte)0x20,
(byte)0x38, (byte)0x9C, (byte)0x21, (byte)0xC3, (byte)0xDC, (byte)0xC8,
(byte)0xA2, (byte)0x4D, (byte)0xC6, (byte)0x2A, (byte)0x35, (byte)0x7F,
(byte)0xF3, (byte)0xA9, (byte)0xE8, (byte)0x1D, (byte)0x7B, (byte)0x2C,
(byte)0x78, (byte)0xFA, (byte)0xB8, (byte)0x02, (byte)0x55, (byte)0x80,
(byte)0x9B, (byte)0xC2, (byte)0xA5, (byte)0xCB,
};
BigInteger bi_p = new BigInteger(pseudoPrime1);
BigInteger bi_q = new BigInteger(pseudoPrime2);
BigInteger bi_pq = (bi_p - 1) * (bi_q - 1);
BigInteger bi_n = bi_p * bi_q;
for (int count = 0; count < rounds; count++)
{
// generate private and public key
BigInteger bi_e = bi_pq.genCoPrime(512, rand);
BigInteger bi_d = bi_e.modInverse(bi_pq);
Console.WriteLine("\ne =\n" + bi_e.ToString(10));
Console.WriteLine("\nd =\n" + bi_d.ToString(10));
Console.WriteLine("\nn =\n" + bi_n.ToString(10) + "\n");
// generate data of random length
int t1 = 0;
while (t1 == 0)
t1 = (int)(rand.NextDouble() * 65);
bool done = false;
while (!done)
{
for (int i = 0; i < 64; i++)
{
if (i < t1)
val[i] = (byte)(rand.NextDouble() * 256);
else
val[i] = 0;
if (val[i] != 0)
done = true;
}
}
while (val[0] == 0)
val[0] = (byte)(rand.NextDouble() * 256);
Console.Write("Round = " + count);
// encrypt and decrypt data
BigInteger bi_data = new BigInteger(val, t1);
BigInteger bi_encrypted = bi_data.modPow(bi_e, bi_n);
BigInteger bi_decrypted = bi_encrypted.modPow(bi_d, bi_n);
// compare
if (bi_decrypted != bi_data)
{
Console.WriteLine("\nError at round " + count);
Console.WriteLine(bi_data + "\n");
return;
}
Console.WriteLine(" <PASSED>.");
}
}
//***********************************************************************
// Performs the calculation of the kth term in the Lucas Sequence.
// For details of the algorithm, see reference [9].
//
// k must be odd. i.e LSB == 1
//***********************************************************************
private static BigInteger[] LucasSequenceHelper(BigInteger P, BigInteger Q,
BigInteger k, BigInteger n,
BigInteger constant, int s)
{
BigInteger[] result = new BigInteger[3];
if ((k.data[0] & 0x00000001) == 0)
throw (new ArgumentException("Argument k must be odd."));
int numbits = k.bitCount();
uint mask = (uint)0x1 << ((numbits & 0x1F) - 1);
// v = v0, v1 = v1, u1 = u1, Q_k = Q^0
BigInteger v = 2 % n, Q_k = 1 % n,
v1 = P % n, u1 = Q_k;
bool flag = true;
for (int i = k.dataLength - 1; i >= 0; i--) // iterate on the binary expansion of k
{
//Console.WriteLine("round");
while (mask != 0)
{
if (i == 0 && mask == 0x00000001) // last bit
break;
if ((k.data[i] & mask) != 0) // bit is set
{
// index doubling with addition
u1 = (u1 * v1) % n;
v = ((v * v1) - (P * Q_k)) % n;
v1 = n.BarrettReduction(v1 * v1, n, constant);
v1 = (v1 - ((Q_k * Q) << 1)) % n;
if (flag)
flag = false;
else
Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
Q_k = (Q_k * Q) % n;
}
else
{
// index doubling
u1 = ((u1 * v) - Q_k) % n;
v1 = ((v * v1) - (P * Q_k)) % n;
v = n.BarrettReduction(v * v, n, constant);
v = (v - (Q_k << 1)) % n;
if (flag)
{
Q_k = Q % n;
flag = false;
}
else
Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
}
mask >>= 1;
}
mask = 0x80000000;
}
// at this point u1 = u(n+1) and v = v(n)
// since the last bit always 1, we need to transform u1 to u(2n+1) and v to v(2n+1)
u1 = ((u1 * v) - Q_k) % n;
v = ((v * v1) - (P * Q_k)) % n;
if (flag)
flag = false;
else
Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
Q_k = (Q_k * Q) % n;
for (int i = 0; i < s; i++)
{
// index doubling
u1 = (u1 * v) % n;
v = ((v * v) - (Q_k << 1)) % n;
if (flag)
{
Q_k = Q % n;
flag = false;
}
else
Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
}
result[0] = u1;
result[1] = v;
result[2] = Q_k;
return result;
}
//***********************************************************************
// Tests the correct implementation of the /, %, * and + operators
//***********************************************************************
public static void MulDivTest(int rounds)
{
Random rand = new Random();
byte[] val = new byte[64];
byte[] val2 = new byte[64];
for (int count = 0; count < rounds; count++)
{
// generate 2 numbers of random length
int t1 = 0;
while (t1 == 0)
t1 = (int)(rand.NextDouble() * 65);
int t2 = 0;
while (t2 == 0)
t2 = (int)(rand.NextDouble() * 65);
bool done = false;
while (!done)
{
for (int i = 0; i < 64; i++)
{
if (i < t1)
val[i] = (byte)(rand.NextDouble() * 256);
else
val[i] = 0;
if (val[i] != 0)
done = true;
}
}
done = false;
while (!done)
{
for (int i = 0; i < 64; i++)
{
if (i < t2)
val2[i] = (byte)(rand.NextDouble() * 256);
else
val2[i] = 0;
if (val2[i] != 0)
done = true;
}
}
while (val[0] == 0)
val[0] = (byte)(rand.NextDouble() * 256);
while (val2[0] == 0)
val2[0] = (byte)(rand.NextDouble() * 256);
Console.WriteLine(count);
BigInteger bn1 = new BigInteger(val, t1);
BigInteger bn2 = new BigInteger(val2, t2);
// Determine the quotient and remainder by dividing
// the first number by the second.
BigInteger bn3 = bn1 / bn2;
BigInteger bn4 = bn1 % bn2;
// Recalculate the number
BigInteger bn5 = (bn3 * bn2) + bn4;
// Make sure they're the same
if (bn5 != bn1)
{
Console.WriteLine("Error at " + count);
Console.WriteLine(bn1 + "\n");
Console.WriteLine(bn2 + "\n");
Console.WriteLine(bn3 + "\n");
Console.WriteLine(bn4 + "\n");
Console.WriteLine(bn5 + "\n");
return;
}
}
}
//***********************************************************************
// Returns the k_th number in the Lucas Sequence reduced modulo n.
//
// Uses index doubling to speed up the process. For example, to calculate V(k),
// we maintain two numbers in the sequence V(n) and V(n+1).
//
// To obtain V(2n), we use the identity
// V(2n) = (V(n) * V(n)) - (2 * Q^n)
// To obtain V(2n+1), we first write it as
// V(2n+1) = V((n+1) + n)
// and use the identity
// V(m+n) = V(m) * V(n) - Q * V(m-n)
// Hence,
// V((n+1) + n) = V(n+1) * V(n) - Q^n * V((n+1) - n)
// = V(n+1) * V(n) - Q^n * V(1)
// = V(n+1) * V(n) - Q^n * P
//
// We use k in its binary expansion and perform index doubling for each
// bit position. For each bit position that is set, we perform an
// index doubling followed by an index addition. This means that for V(n),
// we need to update it to V(2n+1). For V(n+1), we need to update it to
// V((2n+1)+1) = V(2*(n+1))
//
// This function returns
// [0] = U(k)
// [1] = V(k)
// [2] = Q^n
//
// Where U(0) = 0 % n, U(1) = 1 % n
// V(0) = 2 % n, V(1) = P % n
//***********************************************************************
public static BigInteger[] LucasSequence(BigInteger P, BigInteger Q,
BigInteger k, BigInteger n)
{
if (k.dataLength == 1 && k.data[0] == 0)
{
BigInteger[] result = new BigInteger[3];
result[0] = 0; result[1] = 2 % n; result[2] = 1 % n;
return result;
}
// calculate constant = b^(2k) / m
// for Barrett Reduction
BigInteger constant = new BigInteger();
int nLen = n.dataLength << 1;
constant.data[nLen] = 0x00000001;
constant.dataLength = nLen + 1;
constant = constant / n;
// calculate values of s and t
int s = 0;
for (int index = 0; index < k.dataLength; index++)
{
uint mask = 0x01;
for (int i = 0; i < 32; i++)
{
if ((k.data[index] & mask) != 0)
{
index = k.dataLength; // to break the outer loop
break;
}
mask <<= 1;
s++;
}
}
BigInteger t = k >> s;
//Console.WriteLine("s = " + s + " t = " + t);
return LucasSequenceHelper(P, Q, t, n, constant, s);
}
//***********************************************************************
// Returns a value that is equivalent to the integer square root
// of the BigInteger.
//
// The integer square root of "this" is defined as the largest integer n
// such that (n * n) <= this
//
//***********************************************************************
public BigInteger sqrt()
{
uint numBits = (uint)this.bitCount();
if ((numBits & 0x1) != 0) // odd number of bits
numBits = (numBits >> 1) + 1;
else
numBits = (numBits >> 1);
uint bytePos = numBits >> 5;
byte bitPos = (byte)(numBits & 0x1F);
uint mask;
BigInteger result = new BigInteger();
if (bitPos == 0)
mask = 0x80000000;
else
{
mask = (uint)1 << bitPos;
bytePos++;
}
result.dataLength = (int)bytePos;
for (int i = (int)bytePos - 1; i >= 0; i--)
{
while (mask != 0)
{
// guess
result.data[i] ^= mask;
// undo the guess if its square is larger than this
if ((result * result) > this)
result.data[i] ^= mask;
mask >>= 1;
}
mask = 0x80000000;
}
return result;
}
//***********************************************************************
// Returns the modulo inverse of this. Throws ArithmeticException if
// the inverse does not exist. (i.e. gcd(this, modulus) != 1)
//***********************************************************************
public BigInteger modInverse(BigInteger modulus)
{
BigInteger[] p = { 0, 1 };
BigInteger[] q = new BigInteger[2]; // quotients
BigInteger[] r = { 0, 0 }; // remainders
int step = 0;
BigInteger a = modulus;
BigInteger b = this;
while (b.dataLength > 1 || (b.dataLength == 1 && b.data[0] != 0))
{
BigInteger quotient = new BigInteger();
BigInteger remainder = new BigInteger();
if (step > 1)
{
BigInteger pval = (p[0] - (p[1] * q[0])) % modulus;
p[0] = p[1];
p[1] = pval;
}
if (b.dataLength == 1)
singleByteDivide(a, b, quotient, remainder);
else
multiByteDivide(a, b, quotient, remainder);
/*
Console.WriteLine(quotient.dataLength);
Console.WriteLine("{0} = {1}({2}) + {3} p = {4}", a.ToString(10),
b.ToString(10), quotient.ToString(10), remainder.ToString(10),
p[1].ToString(10));
*/
q[0] = q[1];
r[0] = r[1];
q[1] = quotient; r[1] = remainder;
a = b;
b = remainder;
step++;
}
if (r[0].dataLength > 1 || (r[0].dataLength == 1 && r[0].data[0] != 1))
throw (new ArithmeticException("No inverse!"));
BigInteger result = ((p[0] - (p[1] * q[0])) % modulus);
if ((result.data[maxLength - 1] & 0x80000000) != 0)
result += modulus; // get the least positive modulus
return result;
}
//***********************************************************************
// Overloading of unary >> operators
//***********************************************************************
public static BigInteger operator >>(BigInteger bi1, int shiftVal)
{
BigInteger result = new BigInteger(bi1);
result.dataLength = shiftRight(result.data, shiftVal);
if ((bi1.data[maxLength - 1] & 0x80000000) != 0) // negative
{
for (int i = maxLength - 1; i >= result.dataLength; i--)
result.data[i] = 0xFFFFFFFF;
uint mask = 0x80000000;
for (int i = 0; i < 32; i++)
{
if ((result.data[result.dataLength - 1] & mask) != 0)
break;
result.data[result.dataLength - 1] |= mask;
mask >>= 1;
}
result.dataLength = maxLength;
}
return result;
}
//***********************************************************************
// Computes the Jacobi Symbol for a and b.
// Algorithm adapted from [3] and [4] with some optimizations
//***********************************************************************
public static int Jacobi(BigInteger a, BigInteger b)
{
// Jacobi defined only for odd integers
if ((b.data[0] & 0x1) == 0)
throw (new ArgumentException("Jacobi defined only for odd integers."));
if (a >= b) a %= b;
if (a.dataLength == 1 && a.data[0] == 0) return 0; // a == 0
if (a.dataLength == 1 && a.data[0] == 1) return 1; // a == 1
if (a < 0)
{
if ((((b - 1).data[0]) & 0x2) == 0) //if( (((b-1) >> 1).data[0] & 0x1) == 0)
return Jacobi(-a, b);
else
return -Jacobi(-a, b);
}
int e = 0;
for (int index = 0; index < a.dataLength; index++)
{
uint mask = 0x01;
for (int i = 0; i < 32; i++)
{
if ((a.data[index] & mask) != 0)
{
index = a.dataLength; // to break the outer loop
break;
}
mask <<= 1;
e++;
}
}
BigInteger a1 = a >> e;
int s = 1;
if ((e & 0x1) != 0 && ((b.data[0] & 0x7) == 3 || (b.data[0] & 0x7) == 5))
s = -1;
if ((b.data[0] & 0x3) == 3 && (a1.data[0] & 0x3) == 3)
s = -s;
if (a1.dataLength == 1 && a1.data[0] == 1)
return s;
else
return (s * Jacobi(b % a1, a1));
}
//***********************************************************************
// Overloading of the NOT operator (1's complement)
//***********************************************************************
public static BigInteger operator ~(BigInteger bi1)
{
BigInteger result = new BigInteger(bi1);
for (int i = 0; i < maxLength; i++)
result.data[i] = (uint)(~(bi1.data[i]));
result.dataLength = maxLength;
while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
result.dataLength--;
return result;
}
/// <summary>
/// 字符串加密
/// </summary>
/// <param name="source">源字符串 明文</param>
/// <param name="key">密匙</param>
/// <returns>加密遇到错误将会返回原字符串</returns>
public static string EncryptString(string source,string key)
{
string encryptString = string.Empty;
byte[] d;
byte[] n;
try
{
if (!CheckSourceValidate(source))
{
throw new Exception("source string too long");
}
//解析这个密钥
ResolveKey(key, out d, out n);
BigInteger biN = new BigInteger(n);
BigInteger biD = new BigInteger(d);
encryptString= EncryptString(source, biD, biN);
}
catch(Exception e)
{
System.IO.File.AppendAllText("error.log", ""+e);
encryptString = source;
}
return encryptString;
}
//***********************************************************************
// Private function that supports the division of two numbers with
// a divisor that has more than 1 digit.
//
// Algorithm taken from [1]
//***********************************************************************
private static void multiByteDivide(BigInteger bi1, BigInteger bi2,
BigInteger outQuotient, BigInteger outRemainder)
{
uint[] result = new uint[maxLength];
int remainderLen = bi1.dataLength + 1;
uint[] remainder = new uint[remainderLen];
uint mask = 0x80000000;
uint val = bi2.data[bi2.dataLength - 1];
int shift = 0, resultPos = 0;
while (mask != 0 && (val & mask) == 0)
{
shift++; mask >>= 1;
}
//Console.WriteLine("shift = {0}", shift);
//Console.WriteLine("Before bi1 Len = {0}, bi2 Len = {1}", bi1.dataLength, bi2.dataLength);
for (int i = 0; i < bi1.dataLength; i++)
remainder[i] = bi1.data[i];
shiftLeft(remainder, shift);
bi2 = bi2 << shift;
/*
Console.WriteLine("bi1 Len = {0}, bi2 Len = {1}", bi1.dataLength, bi2.dataLength);
Console.WriteLine("dividend = " + bi1 + "\ndivisor = " + bi2);
for(int q = remainderLen - 1; q >= 0; q--)
Console.Write("{0:x2}", remainder[q]);
Console.WriteLine();
*/
int j = remainderLen - bi2.dataLength;
int pos = remainderLen - 1;
ulong firstDivisorByte = bi2.data[bi2.dataLength - 1];
ulong secondDivisorByte = bi2.data[bi2.dataLength - 2];
int divisorLen = bi2.dataLength + 1;
uint[] dividendPart = new uint[divisorLen];
while (j > 0)
{
ulong dividend = ((ulong)remainder[pos] << 32) + (ulong)remainder[pos - 1];
//Console.WriteLine("dividend = {0}", dividend);
ulong q_hat = dividend / firstDivisorByte;
ulong r_hat = dividend % firstDivisorByte;
//Console.WriteLine("q_hat = {0:X}, r_hat = {1:X}", q_hat, r_hat);
bool done = false;
while (!done)
{
done = true;
if (q_hat == 0x100000000 ||
(q_hat * secondDivisorByte) > ((r_hat << 32) + remainder[pos - 2]))
{
q_hat--;
r_hat += firstDivisorByte;
if (r_hat < 0x100000000)
done = false;
}
}
for (int h = 0; h < divisorLen; h++)
dividendPart[h] = remainder[pos - h];
BigInteger kk = new BigInteger(dividendPart);
BigInteger ss = bi2 * (long)q_hat;
//Console.WriteLine("ss before = " + ss);
while (ss > kk)
{
q_hat--;
ss -= bi2;
//Console.WriteLine(ss);
}
BigInteger yy = kk - ss;
//Console.WriteLine("ss = " + ss);
//Console.WriteLine("kk = " + kk);
//Console.WriteLine("yy = " + yy);
for (int h = 0; h < divisorLen; h++)
remainder[pos - h] = yy.data[bi2.dataLength - h];
/*
Console.WriteLine("dividend = ");
for(int q = remainderLen - 1; q >= 0; q--)
Console.Write("{0:x2}", remainder[q]);
Console.WriteLine("\n************ q_hat = {0:X}\n", q_hat);
*/
result[resultPos++] = (uint)q_hat;
pos--;
j--;
}
outQuotient.dataLength = resultPos;
int y = 0;
for (int x = outQuotient.dataLength - 1; x >= 0; x--, y++)
outQuotient.data[y] = result[x];
for (; y < maxLength; y++)
outQuotient.data[y] = 0;
while (outQuotient.dataLength > 1 && outQuotient.data[outQuotient.dataLength - 1] == 0)
outQuotient.dataLength--;
if (outQuotient.dataLength == 0)
outQuotient.dataLength = 1;
outRemainder.dataLength = shiftRight(remainder, shift);
for (y = 0; y < outRemainder.dataLength; y++)
outRemainder.data[y] = remainder[y];
for (; y < maxLength; y++)
outRemainder.data[y] = 0;
}
/// <summary>
/// 用指定的密匙加密
/// </summary>
/// <param name="source">明文</param>
/// <param name="d">可以是RSACryptoServiceProvider生成的D</param>
/// <param name="n">可以是RSACryptoServiceProvider生成的Modulus</param>
/// <returns>返回密文</returns>
private static string EncryptString(string source, BigInteger d, BigInteger n)
{
int len = source.Length;
int len1 = 0;
int blockLen = 0;
if ((len % 128) == 0)
len1 = len / 128;
else
len1 = len / 128 + 1;
string block = "";
StringBuilder result = new StringBuilder();
for (int i = 0; i < len1; i++)
{
if (len >= 128)
blockLen = 128;
else
blockLen = len;
block = source.Substring(i * 128, blockLen);
byte[] oText = System.Text.Encoding.Default.GetBytes(block);
BigInteger biText = new BigInteger(oText);
BigInteger biEnText = biText.modPow(d, n);
string temp = biEnText.ToHexString();
result.Append(temp).Append("@");
len -= blockLen;
}
return result.ToString().TrimEnd('@');
}
//***********************************************************************
// Tests the correct implementation of sqrt() method.
//***********************************************************************
public static void SqrtTest(int rounds)
{
Random rand = new Random();
for (int count = 0; count < rounds; count++)
{
// generate data of random length
int t1 = 0;
while (t1 == 0)
t1 = (int)(rand.NextDouble() * 1024);
Console.Write("Round = " + count);
BigInteger a = new BigInteger();
a.genRandomBits(t1, rand);
BigInteger b = a.sqrt();
BigInteger c = (b + 1) * (b + 1);
// check that b is the largest integer such that b*b <= a
if (c <= a)
{
Console.WriteLine("\nError at round " + count);
Console.WriteLine(a + "\n");
return;
}
Console.WriteLine(" <PASSED>.");
}
}
//***********************************************************************
// Generates a positive BigInteger that is probably prime.
//***********************************************************************
public static BigInteger genPseudoPrime(int bits, int confidence, Random rand)
{
BigInteger result = new BigInteger();
bool done = false;
while (!done)
{
result.genRandomBits(bits, rand);
result.data[0] |= 0x01; // make it odd
// prime test
done = result.isProbablePrime(confidence);
}
return result;
}
static void Main(string[] args)
{
while (true)
{
RSA.BigInteger x = new RSA.BigInteger();
string Mul, Sub, Add;
List <string> ans = new List <string>();
Console.WriteLine("********************RSA Project********************");
string choose;
Console.WriteLine("[1]-Adding Function:");
Console.WriteLine("[2]-Subtract Function:");
Console.WriteLine("[3]-Multiply Function:");
Console.Write("Enter your choose :");
choose = Console.ReadLine();
if (choose == "1")
{
string filepath = "AddTestCases.txt";
List <string> lines = File.ReadAllLines(filepath).ToList();
List <string> fileinput = new List <string>();
foreach (string line in lines)
{
if (line.Length > 0)
{
fileinput.Add(line);
}
}
Add = "Add_output.txt";
/////////////////////////////////////////
Stopwatch cas = Stopwatch.StartNew();
cas.Start();
for (int i = 1; i < fileinput.Count; i += 2)
{
// sw.Start();
ans.Add(x.Add(fileinput[i], fileinput[i + 1]));
if (i + 2 < fileinput.Count)
{
ans.Add("");
}
}
cas.Stop();
Console.WriteLine("case " + " is " + cas.Elapsed);
File.WriteAllLines(Add, ans);
}
else if (choose == "2")
{
string filepath = "SubtractTestCases.txt";
List <string> lines = File.ReadAllLines(filepath).ToList();
List <string> fileinput = new List <string>();
foreach (string line in lines)
{
if (line.Length > 0)
{
fileinput.Add(line);
}
}
Sub = "Sub_output.txt";
Stopwatch cas = Stopwatch.StartNew();
cas.Start();
for (int i = 1; i < fileinput.Count; i += 2)
{
ans.Add(x.subtract(fileinput[i], fileinput[i + 1]));
if (i + 2 < fileinput.Count)
{
ans.Add("");
}
}
cas.Stop();
Console.WriteLine("case " + " is " + cas.Elapsed);
File.WriteAllLines(Sub, ans);
}
else if (choose == "3")
{
string filepath = "MultiplyTestCases.txt";
List <string> lines = File.ReadAllLines(filepath).ToList();
List <string> fileinput = new List <string>();
foreach (string line in lines)
{
if (line.Length > 0)
{
fileinput.Add(line);
}
}
Mul = "Mul_output.txt";
Stopwatch cas = Stopwatch.StartNew();
cas.Start();
for (int i = 1; i < fileinput.Count; i += 2)
{
ans.Add(x.Mul(fileinput[i], fileinput[i + 1]));
if (i + 2 < fileinput.Count)
{
ans.Add("");
}
}
cas.Stop();
Console.WriteLine("case " + " is " + cas.Elapsed);
File.WriteAllLines(Mul, ans);
}
}
}
//***********************************************************************
// Overloading of addition operator
//***********************************************************************
public static BigInteger operator +(BigInteger bi1, BigInteger bi2)
{
BigInteger result = new BigInteger();
result.dataLength = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;
long carry = 0;
for (int i = 0; i < result.dataLength; i++)
{
long sum = (long)bi1.data[i] + (long)bi2.data[i] + carry;
carry = sum >> 32;
result.data[i] = (uint)(sum & 0xFFFFFFFF);
}
if (carry != 0 && result.dataLength < maxLength)
{
result.data[result.dataLength] = (uint)(carry);
result.dataLength++;
}
while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
result.dataLength--;
// overflow check
int lastPos = maxLength - 1;
if ((bi1.data[lastPos] & 0x80000000) == (bi2.data[lastPos] & 0x80000000) &&
(result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000))
{
throw (new ArithmeticException());
}
return result;
}
/// <summary>
/// 字符串解密
/// </summary>
/// <param name="encryptString">密文</param>
/// <param name="key">密钥</param>
/// <returns>遇到解密失败将会返回原字符串</returns>
public static string DecryptString(string encryptString, string key)
{
string source = string.Empty;
byte[] e;
byte[] n;
try
{
//解析这个密钥
ResolveKey(key, out e, out n);
BigInteger biE = new BigInteger(e);
BigInteger biN = new BigInteger(n);
source = DecryptString(encryptString, biE, biN);
}
catch (Exception ex){
System.IO.File.AppendAllText("error.log", ""+ex);
source = encryptString;
}
return source;
}
//***********************************************************************
// Overloading of the unary ++ operator
//***********************************************************************
public static BigInteger operator ++(BigInteger bi1)
{
BigInteger result = new BigInteger(bi1);
long val, carry = 1;
int index = 0;
while (carry != 0 && index < maxLength)
{
val = (long)(result.data[index]);
val++;
result.data[index] = (uint)(val & 0xFFFFFFFF);
carry = val >> 32;
index++;
}
if (index > result.dataLength)
result.dataLength = index;
else
{
while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
result.dataLength--;
}
// overflow check
int lastPos = maxLength - 1;
// overflow if initial value was +ve but ++ caused a sign
// change to negative.
if ((bi1.data[lastPos] & 0x80000000) == 0 &&
(result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000))
{
throw (new ArithmeticException("Overflow in ++."));
}
return result;
}
/// <summary>
/// 用指定的密匙加密
/// </summary>
/// <param name="source">密文</param>
/// <param name="e">可以是RSACryptoServiceProvider生成的Exponent</param>
/// <param name="n">可以是RSACryptoServiceProvider生成的Modulus</param>
/// <returns>返回明文</returns>
private static string DecryptString(string encryptString, BigInteger e, BigInteger n)
{
StringBuilder result = new StringBuilder();
string[] strarr1 = encryptString.Split(new char[] { '@' }, StringSplitOptions.RemoveEmptyEntries);
for (int i = 0; i < strarr1.Length; i++)
{
string block = strarr1[i];
BigInteger biText = new BigInteger(block, 16);
BigInteger biEnText = biText.modPow(e, n);
string temp = System.Text.Encoding.Default.GetString(biEnText.getBytes());
result.Append(temp);
}
return result.ToString();
}
//***********************************************************************
// Overloading of subtraction operator
//***********************************************************************
public static BigInteger operator -(BigInteger bi1, BigInteger bi2)
{
BigInteger result = new BigInteger();
result.dataLength = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;
long carryIn = 0;
for (int i = 0; i < result.dataLength; i++)
{
long diff;
diff = (long)bi1.data[i] - (long)bi2.data[i] - carryIn;
result.data[i] = (uint)(diff & 0xFFFFFFFF);
if (diff < 0)
carryIn = 1;
else
carryIn = 0;
}
// roll over to negative
if (carryIn != 0)
{
for (int i = result.dataLength; i < maxLength; i++)
result.data[i] = 0xFFFFFFFF;
result.dataLength = maxLength;
}
// fixed in v1.03 to give correct datalength for a - (-b)
while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
result.dataLength--;
// overflow check
int lastPos = maxLength - 1;
if ((bi1.data[lastPos] & 0x80000000) != (bi2.data[lastPos] & 0x80000000) &&
(result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000))
{
throw (new ArithmeticException());
}
return result;
}